Smart sensor measures the local heat flux in a turbulent system

Convection—the rising of warm, buoyant fluid through cooler, denser fluid—occurs in the oceans, the atmosphere, Earth’s core and mantle, the stars, heated beakers and pots, and uncountable other natural and industrial systems. Despite that ubiquity, our understanding of the process remains incomplete, at least when the system is driven hard enough to become turbulent. To study the problem, researchers often turn to an idealized experiment: the Rayleigh—Bénard convection cell, a container of fluid heated from below and cooled from above.

The temperature gradient drives the convection. As hot, coherent plumes of fluid rise upward due to the buoyant force, they push aside material above them. Similarly, cold plumes detached from a thin layer at the top push aside material as they fall. The deflection of material, whether in a cell the size of a soda can or a swimming pool, sets up a thermal “wind” that circulates the upwelling and downwelling jets around the walls of the cell. Because the plumes carry hotter or colder fluid than what’s around them, their shapes and sizes can be imaged. The variations in density produce concomitant variations in the index of refraction, so light illuminating the cell creates bright lines and shadows known as shadowgraphs (see the article by Leo Kadanoff in Physics Today, August 2001, page 34 ).

To get a more quantitative description of pattern and structure, researchers have conventionally measured properties like fluid temperature or velocity by placing probes at fixed points in the flow or by seeding the fluid with tiny fluorescing or reflecting beads and then monitoring the flow from a stationary reference frame. An alternative approach, one more naturally suited to mixing processes, is to measure properties in the local reference frame of a fluid element itself. That so-called Lagrangian approach has been applied to large-scale flows—think atmospheric balloons or untethered ocean floats—but is harder to implement in the lab.

Jean-François Pinton and colleagues from CNRS and the École Normale Supérieure in Lyon, France, have now developed a mobile sensor sophisticated enough to measure the local temperature—to within a thousandth of a degree—and yet small and passive enough to be swept up in the flow of a Rayleigh—Bénard cell. ¹ Their proof-of-principle measurement, illustrated here, is akin to a time-lapse photograph; it reveals the temperature at each point along the counterclockwise trajectory traced out by the sensor over some 3500 seconds.

A digital camera tracked the trajectory in the cell, a thin, water-filled, glass container (10 cm × 40 cm × 40 cm). That allowed the team to calculate the local heat flux, a product of the liquid’s temperature deviation from the mean and its velocity. The challenge was ensuring that the sensor could faithfully follow the flow. Woodrow Shew, then a postdoc in Pinton’s lab, packed an RF emitter, antenna, and lithium battery into a marble-sized plastic sphere whose surface is covered by four thermistors. That size is too large to probe the thin boundary layers of hot and cold fluid at the top and bottom of the cell, but small enough, he says, to be entrained within a plume; shadowgraphs showed that most plumes were larger than the 17-mm-wide sensor. To match the water’s density to within 1% of the sensor’s, he added minute amounts of glycerol to the water. But the slight density offset, along with size, heat capacity, and viscosity effects, may, Shew concedes, influence how passive the sensor really is.

Still, its temperature and velocity are strongly correlated with each other and bear out the dynamics of turbulent flow. The thermal wind presses rising or falling plumes toward the side walls. They eventually splash against the top or bottom boundary layer and unleash new plumes. The sensor is thought to ride one plume at a time during the roughly 100 seconds it takes the wind to circulate around the cell. In that interpretation, the sensor typically samples one plume transporting the heat upward, and gets entrained in another carrying cold fluid downward. The dynamics of its getting caught and uncaught are unclear, though, as a plume may decay out from underneath the sensor during turbulent mixing of heat with nearby fluid. Only once during the sensor’s hour-long measurement did it follow the looping flow into the center, where the water moves slowly and temperatures should be well mixed.

Although the sensor’s motion is quasi-periodic, its temperature fluctuates widely and irregularly: Different plumes vary widely in the amount of heat they carry. And the Lyon group’s calculation of the Nusselt number, the ratio of the heat transported by the plumes to that transported by diffusive mixing, confirms the dominant role plumes play in the cell. They transport over 4 times more heat than the rest of the fluid motion, and often as much as 20 times more.

The researchers’ demonstration, says Eberhard Bodenschatz of the Max Planck Institute for Dynamics and Self-Organization, sets the stage for developing smart sensors of all kinds. “With advances in miniaturization, the potential is enormous. Imagine measuring local accelerations, pressure variations, chemical compositions, or magnetic fields, for instance, as a fluid becomes mixed.” Pinton’s group, it turns out, is already fitting its device with tiny accelerometers.